?lahef

Computes a partial factorization of a complex Hermitian indefinite matrix, using the diagonal pivoting method.

Syntax

call clahef( uplo, n, nb, kb, a, lda, ipiv, w, ldw, info )

call zlahef( uplo, n, nb, kb, a, lda, ipiv, w, ldw, info )

Include Files

  • Fortran: mkl.fi
  • C: mkl.h

Description

The routine ?lahef computes a partial factorization of a complex Hermitian matrix A, using the Bunch-Kaufman diagonal pivoting method. The partial factorization has the form:


Equation


Equation

where the order of D is at most nb.

The actual order is returned in the argument kb, and is either nb or nb-1, or n if nnb.

Note that UH denotes the conjugate transpose of U.

This is an auxiliary routine called by ?hetrf. It uses blocked code (calling Level 3 BLAS) to update the submatrix A11 (if uplo = 'U') or A22 (if uplo = 'L').

Input Parameters

uplo

CHARACTER*1.

Specifies whether the upper or lower triangular part of the Hermitian matrix A is stored:

= 'U': upper triangular

= 'L': lower triangular

n

INTEGER. The order of the matrix A. n 0.

nb

INTEGER. The maximum number of columns of the matrix A that should be factored. nb should be at least 2 to allow for 2-by-2 pivot blocks.

a

COMPLEX for clahef

DOUBLE COMPLEX for zlahef.

Array, DIMENSION (lda, n).

On entry, the Hermitian matrix A.

If uplo = 'U', the leading n-by-n upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced.

If uplo = 'L', the leading n-by-n lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced.

lda

INTEGER. The leading dimension of the array a. lda max(1,n).

w

COMPLEX for clahef

DOUBLE COMPLEX for zlahef.

Workspace array, DIMENSION (ldw, nb).

ldw

INTEGER. The leading dimension of the array w. ldw max(1,n).

Output Parameters

kb

INTEGER. The number of columns of A that were actually factored kb is either nb-1 or nb, or n if nnb.

a

On exit, A contains details of the partial factorization.

ipiv

INTEGER.

Array, DIMENSION (n ). Details of the interchanges and the block structure of D.

If uplo = 'U', only the last kb elements of ipiv are set;

if uplo = 'L', only the first kb elements are set.

If ipiv(k) > 0, then rows and columns k and ipiv(k) are interchanged and D(k, k) is a 1-by-1 diagonal block.

If uplo = 'U' and ipiv(k) = ipiv(k-1) < 0, then rows and columns k-1 and -ipiv(k) are interchanged and D(k-1:k, k-1:k) is a 2-by-2 diagonal block.

If uplo = 'L' and ipiv(k) = ipiv(k+1) < 0, then rows and columns k+1 and -ipiv(k) are interchanged and D( k:k+1, k:k+1) is a 2-by-2 diagonal block.

info

INTEGER.

= 0: successful exit

> 0: if info = k, D(k, k) is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular.

For more complete information about compiler optimizations, see our Optimization Notice.